Let's solve this step by step:

1. Let's assume the original two-digit number is 10x + y, where x and y are the tens and units digits respectively.

2. The number obtained by interchanging the digits will be 10y + x.

3. According to the problem, the original number is 63 more than the number obtained by interchanging the digits. So, we can write the equation as: 10x + y = 63 + 10y + x.

4. Simplifying this equation gives: 9x - 9y = 63.

5. Dividing through by 9 gives: x - y = 7.

6. The problem also states that the sum of the digits of the number is 11. So, we can write the equation as: x + y = 11.

7. Now we have a system of two equations: x - y = 7 and x + y = 11.

8. Adding these two equations gives: 2x = 18, so x = 9.

9. Substituting x = 9 into the equation x + y = 11 gives: 9 + y = 11, so y = 2.

10. Therefore, the original number is 92.

Question

Let's solve this step by step:

1. Let's assume the original two-digit number is 10x + y, where x and y are the tens and units digits respectively.

2. The number obtained by interchanging the digits will be 10y + x.

3. According to the problem, the original number is 63 more than the number obtained by interchanging the digits. So, we can write the equation as: 10x + y = 63 + 10y + x.

4. Simplifying this equation gives: 9x - 9y = 63.

5. Dividing through by 9 gives: x - y = 7.

6. The problem also states that the sum of the digits of the number is 11. So, we can write the equation as: x + y = 11.

7. Now we have a system of two equations: x - y = 7 and x + y = 11.

8. Adding these two equations gives: 2x = 18, so x = 9.

9. Substituting x = 9 into the equation x + y = 11 gives: 9 + y = 11, so y = 2.

10. Therefore, the original number is 92.

Knowee AI · Accepted Answer

Let's solve this step by step:

1. Let's assume the original two-digit number is 10x + y, where x and y are the tens and units digits respectively.

2. The number obtained by interchanging the digits will be 10y + x.

3. According to the problem, the original number is 63 more than the number obtained by interchanging the digits. So, we can write the equation as: 10x + y = 63 + 10y + x.

4. Simplifying this equation gives: 9x - 9y = 63.

5. Dividing through by 9 gives: x - y = 7.

6. The problem also states that the sum of the digits of the number is 11. So, we can write the equation as: x + y = 11.

7. Now we have a system of two equations: x - y = 7 and x + y = 11.

8. Adding these two equations gives: 2x = 18, so x = 9.

9. Substituting x = 9 into the equation x + y = 11 gives: 9 + y = 11, so y = 2.

10. Therefore, the original number is 92.

The number obtained by interchanging the digits of a two-digit number is less than the original number by 63. If the sum of the digits of the number is 11, what is the original number?

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